One of the comments from the source....
“I suppose I should look at the J Math Phys article. However, their variational bound approaches the Bohr classical model in the limit of large n with circular orbits. Why is it surprising that such a limit would involve pi?”
I guess what he is saying is that since the model for hydrogen has electrons in circular orbits it shouldn’t be surprising to find pi in the calculations.
“They found that the limit of the variational solution approaches the model of hydrogen developed by physicist Niels Bohr in the early 20th century, which depicts the orbits of the electron as perfectly circular.”
Yeah - when I hit that line in the article I thought “Well duh - pi is going to get involved.”
Still though - cool article. I think it might be more an article on the link between classical and quantum physics than anything else.